Plasticity (physics)
From Wikipedia, the free encyclopedia
| General |
| Solid mechanics |
|
| Fluid mechanics |
- For other uses, see Plasticity.
In physics and materials science, plasticity is a property of a material to undergo a non-reversible change of shape in response to an applied force. Plastic deformation occurs under shear stress, as opposed to brittle fractures which occur under normal stress. Examples of plastic materials are clay and mild steel. In engineering, the transition from elastic behavior to plastic behavior is called yield.
Contents |
[edit] Explanation
For many ductile metals, tensile loading applied to a sample will cause it to behave in an elastic manner. Each increment of load is accompanied by a proportional increment in extension, and when the load is removed, the piece returns exactly to its original size. However, once the load exceeds some threshold (the yield strength), the extension increases more rapidly than in the elastic region, and when the load is removed, some amount of the extension remains. A generic graph displaying this behaviour is below.
Plasticity is a property of materials to undergo large deformation without fracture. This is found in most metals, and in general is a good description of a large class of materials. Perfect plasticity is a property of materials to undergo large shear deformation without any increase of (shear) stress. Plastic materials that are not perfectly plastic are visco-plastic.
Microscopically, plasticity is a consequence of dislocations.
[edit] Mathematical descriptions of Plasticity
[edit] Deformation theory
There are several mathematical descriptions of Plasticity. One is deformation theory (see e.g. Hooke's law)where the stress tensor (of order d in d dimensions) is a function of the strain tensor. Although this description is acccurate when a small part of mater is subjected to increasing loading (such as strain loading),this theory can not account for irreversibility.
The image above represents a shear stress component with respect to a shear strain component, under increasing strain loading.
Ductile materials can sustain large plastic deformations without fracture. However, even ductile metals will fracture when the strain becomes large enough - this is as a result of work-hardening of the material, which causes it to become brittle. Heat treatment such as annealing can restore the ductility of a worked piece, so that shaping can continue.
[edit] Flow plasticty theory
In 1934, Egon Orowan, Michael Polanyi and Geoffrey Ingram Taylor, roughly simultaneously, realized that the plastic deformation of ductile materials could be explained in terms of the theory of dislocations. The more correct mathematical theory of plasticty, flow plasticty theory, uses a set of non-linear, non-integratable equations to describe the set of changes on strain and stress with respect to a previous state and a small increase of deformation.
[edit] Martensitic materials
Some materials, especially those prone to Martensitic transformations, deform in ways that are not well described by the classic theories of plasticity and elasticity. One of the best-known examples of this is nitinol, which exhibits pseudoelasticity: deformations which are reversible in the context of mechanical design, but irreversible in terms of thermodynamics.
[edit] References
- R. Hill, The Mathematical Theory of Plasticity (1998), Oxford University Press, USA, ISBN 0-19-850367-9 (Old but classic)
- Jacob Lubliner, Plasticity theory (1990), Macmillan Publishing, New York ISBN 0-02-372161-8 (Provides general overview)
- L. M. Kachanov, Fundamentals of the Theory of Plasticity, Dover Books (General overview)
- J. C. Simo, Thomas J. Hughes ,Computational Inelasticity, Springer
|
Classical mechanics | Electromagnetism | Thermodynamics | General relativity | Quantum mechanics | |
|
Particle physics | Condensed matter physics | Atomic, molecular, and optical physics | |
fr:Déformation plastique it:Plasticità (fisica) ja:塑性 pl:Plastyczność
